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CHOL Cholesky factorization. R = CHOL(A) calculates the Cholesky factor of full or sparse A using the diagonal and upper triangle of A, such that A = R'*R. A must be positive definite, and the lower triangle is assumed to be the (complex conjugate) transpose of the upper triangle. R = CHOL(A,TRIANGLE) specifies which triangle of A to use. For example, if TRIANGLE is 'lower', then CHOL uses only the diagonal and lower triangle of A to produce a lower triangular R such that A = R*R'. The default value of TRIANGLE is 'upper'. Using the 'lower' option is equivalent to calling CHOL with the 'upper' option and the transpose of A, and then transposing the output matrix R. In the following syntaxes, the output R is described only for the case when TRIANGLE is 'upper'. [R,FLAG] = CHOL(___) also returns the output FLAG indicating whether A is positive definite. Use this syntax to suppress errors produced when A is not positive definite. * If A is positive definite, then FLAG is 0 and R is the same as above. * If A is not positive definite, then FLAG is a positive integer. - If A is full, then R is an upper triangular matrix of size q = FLAG-1 such that R'*R = A(1:q,1:q). - If A is sparse, then R is an upper triangular matrix of size q-by-n such that the L-shaped region of the first q rows and first q columns of R'*R agree with those of A. [R,FLAG,P] = CHOL(S), for sparse S, additionally returns a permutation matrix P, which is a preordering of S obtained by AMD. The Cholesky factor of P'*S*P tends to be sparser than that of S. If FLAG = 0, then R is an upper triangular matrix such that R'*R = P'*S*P. [R,FLAG,p] = CHOL(___,OUTPUTFORM) specifies whether to return the permutation information as a vector p or matrix P. With this syntax you must specify a sparse input matrix S, and you optionally can specify TRIANGLE. For example, if OUTPUTFORM is 'vector' and FLAG = 0, then S(p,p) = R'*R. The default value of OUTPUTFORM is 'matrix' such that P'*S*P = R'*R. See also CHOLUPDATE, ICHOL, LDL, LU. Documentation for chol doc chol Other functions named chol codistributed/chol gpuArray/chol sym/chol